\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t51\_bcialg\_5 (TMZ12FXnnkujNWadyZLPcPzoXv89PS8UjZC)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_bcialg\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v11\_bcialg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_bcialg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_bcialg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~X0){\unicdcdcdhd}((\\
v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}((v11\_bcialg\_3~\\
X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))))){\unicdbdjded}((v8\_bcialg\_1~X0){\unicdcdcdhd}(m1\_bcialg\_5~\\
X0~np\_\_1~k6\_numbers~k6\_numbers~k6\_numbers)))\end{array}
\label{hyp:ehfdadpfcgdgjgbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~X0){\unicdcdcdhd}((\\
v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}((v10\_bcialg\_3~\\
X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))))){\unicdbdjded}((v8\_bcialg\_1~X0){\unicdcdcdhd}(m1\_bcialg\_5~\\
X0~k6\_numbers~np\_\_1~k6\_numbers~np\_\_1)))\end{array}
\label{hyp:ehedjdpfcgdgjgbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~X0){\unicdcdcdhd}((\\
v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}((v1\_bcialg\_3~\\
X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))))){\unicdbdjded}(m1\_bcialg\_5~X0~k6\_numbers~k6\_numbers~\\
k6\_numbers~k6\_numbers))\end{array}
\label{hyp:ehddidpfcgdgjgbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}\\
(l2\_bcialg\_1~X0))))))){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}\\
((v4\_bcialg\_1~X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~\\
X0){\unicdcdcdhd}((v11\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))))){\unicdbdjded}(((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}\\
((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}((v1\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_1~\\
X0)))))))){\unicdcdcdhd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}\\
((v10\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0))))))))))\end{array}
\label{hyp:ehddedpfcgdgjgbgmghgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfcgdgjgbgmghgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
(((v8\_bcialg\_1~X0){\unicdcdcdhd}(m1\_bcialg\_5~X0~np\_\_1~k6\_numbers~k6\_numbers~\\
k6\_numbers)){\unicdbdjded}(((v8\_bcialg\_1~X0){\unicdcdcdhd}(m1\_bcialg\_5~X0~k6\_numbers~\\
k6\_numbers~k6\_numbers~k6\_numbers)){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}(m1\_bcialg\_5~\\
X0~k6\_numbers~np\_\_1~k6\_numbers~np\_\_1))))\end{array}$$
\end{theorem}
\end{document}
